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edmf [2021/01/22 22:21] – external edit 127.0.0.1edmf [2022/09/14 17:47] (current) – ibartolo
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 where subgrid $tc$ indicates turbulence and convection, the overline indicates a horizontal Reynolds' average, and the prime a perturbation from this mean. Ever since the advent of numerical simulation of atmospheric flow the closure of the flux $\overline{w'\phi'}$ has been subject to intense research, and many different methods have been proposed. At the foundation of most schemes are two basic transport models. The first is the //Eddy Diffusive// (ED) transport model which describes the behavior by small-scale turbulent processes, acting to even out differences.  where subgrid $tc$ indicates turbulence and convection, the overline indicates a horizontal Reynolds' average, and the prime a perturbation from this mean. Ever since the advent of numerical simulation of atmospheric flow the closure of the flux $\overline{w'\phi'}$ has been subject to intense research, and many different methods have been proposed. At the foundation of most schemes are two basic transport models. The first is the //Eddy Diffusive// (ED) transport model which describes the behavior by small-scale turbulent processes, acting to even out differences. 
 \begin{eqnarray*} \begin{eqnarray*}
-\overline{w'\phi'}_{\mbox{\tiny ED}} \sim - K_{\phi} \frac{\partial \overline{\phi}}{\partial z}+\overline{w'\phi'}_{ED} \sim - K_{\phi} \frac{\partial \overline{\phi}}{\partial z}
 \end{eqnarray*} \end{eqnarray*}
 where $K_{\phi}$ is the eddy diffusivity coefficient. As expressed by the dependence on the vertical gradient, in principle this model acts purely down-gradient, and can not penetrate inversions very deeply. The second basic transport model is //advective//, and describes the behavior of larger-scale convective motions (or plumes) that have enough inertia to overcome stable layers, where $K_{\phi}$ is the eddy diffusivity coefficient. As expressed by the dependence on the vertical gradient, in principle this model acts purely down-gradient, and can not penetrate inversions very deeply. The second basic transport model is //advective//, and describes the behavior of larger-scale convective motions (or plumes) that have enough inertia to overcome stable layers,
 \begin{eqnarray*} \begin{eqnarray*}
-\overline{w'\phi'}_{\mbox{\tiny MF}} \approx M_c \left( \phi_c -\phi_e \right)+\overline{w'\phi'}_{MF} \approx M_c \left( \phi_c -\phi_e \right)
 \end{eqnarray*} \end{eqnarray*}
 where $M_c$ is the volumetric //Mass Flux// (MF) by the convective elements, defined (in approximation) as the product of their area fraction and their vertical velocity. Such motions can transport in counter-gradient directions, and can maintain differences between a convective plume ( c) and its environment (e) for some time. The Eddy Diffusivity - Mass Flux (EDMF) approach is a relatively new method that aims to combine the benefits of both ways of describing transport, where $M_c$ is the volumetric //Mass Flux// (MF) by the convective elements, defined (in approximation) as the product of their area fraction and their vertical velocity. Such motions can transport in counter-gradient directions, and can maintain differences between a convective plume ( c) and its environment (e) for some time. The Eddy Diffusivity - Mass Flux (EDMF) approach is a relatively new method that aims to combine the benefits of both ways of describing transport,
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 An ensemble of plumes can be differentiated based on updraft properties such as thermodynamic state, vertical velocity or buoyancy. Alternatively one can define a plume spectrum in size-space, as schematically illustrated in Fig. 4. This has some important consequences. For example, the size distribution of plume properties becomes the foundation of the EDMF framework. This can be understood by rewriting the multi-plume MF flux at some height $z$ as a function of plume size $l$, An ensemble of plumes can be differentiated based on updraft properties such as thermodynamic state, vertical velocity or buoyancy. Alternatively one can define a plume spectrum in size-space, as schematically illustrated in Fig. 4. This has some important consequences. For example, the size distribution of plume properties becomes the foundation of the EDMF framework. This can be understood by rewriting the multi-plume MF flux at some height $z$ as a function of plume size $l$,
 \begin{eqnarray*} \begin{eqnarray*}
-\overline{w' \phi'}_{\mbox{\tiny MF}}(z) +\overline{w' \phi'}_{MF}(z) 
 & \approx & \int_{l} \mathcal{M}(l,z) \left[ \phi(l,z) - \phi_e(z) \right] dl \\ & \approx & \int_{l} \mathcal{M}(l,z) \left[ \phi(l,z) - \phi_e(z) \right] dl \\
 & = &  \int_{l} \mathcal{A}(l,z) \left[ w(l,z) - w_e(z) \right] \left[ \phi(l,z) - \phi_e(z) \right] dl & = &  \int_{l} \mathcal{A}(l,z) \left[ w(l,z) - w_e(z) \right] \left[ \phi(l,z) - \phi_e(z) \right] dl
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 ==== Contact ===== ==== Contact =====
  
-For more information get in contact with [[http://www.geomet.uni-koeln.de/das-institut/mitarbeiter/griewank/|Philipp Griewank]] or [[http://www.geomet.uni-koeln.de/das-institut/mitarbeiter/neggers/|Roel Neggers]]. +For more information get in contact with [[http://www.geomet.uni-koeln.de/das-institut/mitarbeiter/neggers/|Roel Neggers]].
  
edmf.1611350494.txt.gz · Last modified: 2021/01/22 22:21 by 127.0.0.1